Question #efef9

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Question #efef9

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Answer 1 · 2017-12-20T07:09:55

$\sqrt{1 - sin x} = sin (\frac{x}{2}) - cos (\frac{x}{2})$ $sqrt(1-sinx)=sin(x/2)-cos(x/2)$

Explanation:

$\sqrt{1 - sin x} = \sqrt{{sin}^{2} (\frac{x}{2}) + {cos}^{2} (\frac{x}{2}) - 2 . sin (\frac{x}{2}) cos (\frac{x}{2})}$ $sqrt(1-sinx)=sqrt(sin^2(x/2)+cos^2(x/2)-2.sin(x/2)cos(x/2)$ $[A s . {sin}^{2} θ + {cos}^{2} θ = 1 and sin 2 θ = 2 sin θ cos θ]$ $color(green)([As.sin^2theta+cos^2theta=1andsin2theta=2sinthetacostheta])$

$= \sqrt{{(sin (\frac{x}{2}) - cos (\frac{x}{2}))}^{2}}$ $=sqrt((sin(x/2)-cos(x/2))^2$ $[A s . a^{2} + b^{2} - 2 a b = {(a - b)}^{2} = {(b - a)}^{2}]$ $color(red)([As.a^2+b^2-2ab=(a-b)^2=(b-a)^2])$

$= sin (\frac{x}{2}) - cos (\frac{x}{2})$ $=sin(x/2)-cos(x/2)$ $(A n s .)$ $color(brown)((Ans.))$

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